Question

Burnett Corp. pays a constant $20 dividend on its stock. The company will maintain this dividend for the next 12 years and will then cease paying dividends forever.If the required return on this stock is 6 percent, what is the current share price?

• $167.68

• $177.74

• $164.32

• $240.00

• $176.06

Answer 1

Solution:

As per the information given in the question Burnett Corp. pays $ 20 constant dividend for the next 12 years.

After 12 years the company will cease to pay dividends forever.

Thus the current share price of the dividend = Present value of the dividends for 12 years at 6 %

This constant dividend is similar to an Ordinary annuity payment.

Thus the formula for calculating the present value of an ordinary annuity :

PV = A * [ ( 1 - ( 1 / ( 1 + r ) ⁿ )) / r ]

Where

PV = Present value of annuity   ;   A = Amount of annuity   ;   r = rate of interest ; n = no. of years

As per the information given in the question we have

r = 6 % = 0.06   ; n = 12 years   ; A = $ 20

Applying the above information in the formula we have

= $ 20 * [ ( 1 - ( 1 / ( 1 + 0.06 ) ¹² )) / 0.06 ]

= $ 20 * [ ( 1 - ( 1 / ( 1.06 ) ¹² )) / 0.06 ]

= $ 20 * [ ( 1 - ( 1 / 2.012196 )) / 0.06 ]

= $ 20 * [ ( 1 – 0.496969 ) / 0.06 ]

= $ 20 * [ 0.503031 / 0.06 ]

= $ 20 * 8.383844

= $ 167.676879

= $ 167.68   ( When rounded off to two decimal places )

Thus the current share price = $ 167.68

The solution is Option 1 = $ 167.68

Note: The value of ( 1.06 ) ¹²   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.06,12) = 2.012196